They managed to keep things level until half-time, but goals from Bertrand Traore, Houssem Aouar and Memphis Depay in the second period rounded off a miserable day for Everton, who saw Morgan Schneiderlin sent off and Cuco Martina taken to hospital after a nasty fall.
Full-back Martina was believed to have sustained a concussion, but the club confirmed hours later that he had been released and would travel back with the squad.
Unsworth, who appears increasingly unlikely to get the job on a full-time basis, though, was left exasperated at full-time.
"It's not about me," he told reporters. "It's about the football club. It's about getting over this disappointing result.
"We can't cave in the way we do when we concede a goal. We need to rectify that very, very quickly.
"I'm really disappointed with the result. For nearly 70 minutes we were nearly perfect with our game plan. If you concede, for five or 10 minutes you all come together and don't concede again.
"When you're not winning games you do concede sloppy goals. The mentality must be stronger and we must have courage if we go a goal behind.
"We have got to pick ourselves up really, really quickly. Sunday is a huge game for me, huge game for the club and I've left the players in no uncertain terms that it's a huge game for them."
DU: "We can't cave in the way we do when we concede a goal. We need to rectify that very, very quickly." pic.twitter.com/mWstPnI9i4— Everton (@Everton) November 2, 2017
Unsworth was less assertive when asked about the situation regarding the manager's job at Everton, simply saying he will accept whatever decision the club makes.
"What will be, will be," he told BT Sport. "Whatever is best for Everton, I'll accept."